By Hall E. H.
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Additional resources for An Electron Theory of Electric Conduction in Metals
Thus an abrupt transition from a point attractor to a stable limit cycle occurs. (D2) Homoclinic bifurcation In Fig. 9(b), as k increases, a homoclinic orbit (a saddle-to-saddle loop consisting in two coinciding branches of the stable and the unstable manifolds of the saddle-point) is formed at k = k0 . From this homoclinic connection a stable limit cycle bifurcates. Here the saddle-point does not disappear. Since the limit-cycle attractor appears “out of the blue sky”, this bifurcation has also been termed the blue-sky catastrophe.
G. Ginzburg–Landau amplitude equations (Falcke et al. 1995, Falcke and Neufeld 1997, Battogtokh and Mikhailov 1996), arrays of discrete oscillators (Pikovsky et al. 1996), reaction–diffusion systems (Ohta 1989, Ohta et al. 1990, Elmer 1990, 1992, Schimansky-Geier et al. 1991, 1992, Engel et al. 1996, Niedernostheide et al. 1997, Hempel et al. 1998), surface reactions (B¨ar et al. 1994, Falcke and Engel 1994) and electro-chemical systems (Mazouz et al. 1997, Wang et al. 2000). For instance, in chemical surface reactions, the pressure of the gas phase, which is the same over the whole surface, represents such a global constraint.
The activator is generally an internal dynamic variable that triggers the instability via an autocatalytic process. Examples are provided by the carrier (electron or hole) density in doped semiconductors. 4 Activator–inhibitor kinetics 31 across the bandgap or from localized levels is an autocatalytic process that leads to a multiplication of the number of carriers. 43) where e and h denote free electrons and holes, respectively, and et and ht stand for electrons and holes trapped at impurities (donors, acceptors, or deep levels).
An Electron Theory of Electric Conduction in Metals by Hall E. H.